Ab initio molecular dynamics: Theory and Implementation

ut all three ab initio approaches to molecular dynamics are contrasted and partlycompared. The important issue of how to obtain the correct forces in these schemesis discussed in some depth. The most popular electronic structure theories implementedwithin ab initio molecular dynamics, density functional theory in the firstplace but also the Hartree–Fock approach, are sketched. Some attention is alsogiven to another important ingredient in ab initio molecular dynamics, the choiceof the basis set.Concerning the depth, the focus of the present discussion is clearly the implementationof both the basic Car–Parrinello and Born–Oppenheimer moleculardynamics schemes in the CPMD package 142 . The electronic structure approachin CPMD is Hohenberg–Kohn–Sham density functional theory within a plane wave/ pseudopotential implementation and the Generalized Gradient Approximation.The formulae for energies, forces, stress, pseudopotentials, boundary conditions,optimization procedures, parallelization etc. are given for this particular choice tosolve the electronic structure problem. One should, however, keep in mind thata variety of other powerful ab initio molecular dynamics codes are available (forinstance CASTEP 116 , CP-PAW 143 , fhi98md 189 , NWChem 446 , VASP 663 ) which arepartly based on very similar techniques. The classic Car–Parrinello approach 108is then extended to other ensembles than the microcanonical one, other electronicstates than the ground state, and to a fully quantum–mechanical representation ofthe nuclei. Finally, the wealth of problems that can be addressed using ab initiomolecular dynamics is briefly sketched at the end, which also serves implicitly asthe “Summary and Conclusions” section.2 Basic Techniques: Theory2.1 Deriving Classical Molecular DynamicsThe starting point of the following discussion is non–relativistic quantum mechanicsas formalized via the time–dependent Schrödinger equationi∂∂t Φ({r i}, {R I }; t) = HΦ({r i }, {R I }; t) (1)in its position representation in conjunction with the standard HamiltonianH = − ∑ I22M I∇ 2 I − ∑ i2∇ 2 i + ∑ 2m e |r i − r j | − ∑ e 2 Z I|R I − r i | + ∑ e 2 Z I Z J|R I − R J |i